That's exactly why you're not supposed to go to the stairwell. That's where the deathly smoke is. Apartment doors are spec'd to keep fire and smoke out. Plus apartment windows must be openable. Ventilation systems are designed not to circulate air between apartments.
Seems like smart design, though two stairwells still seems useful too? But if the strategy is huddle in place and smoke-sealed doors, maybe not.
But I have A question from your PoV as a resident if London w/ more "on the ground knowledge" outside of normal media reports: What happened with Grenfell tower to go so wrong?